Question

The student in the previous example also wants to estimate the proportion of cities that have
private refuse collectors. The students wants to estimate the population proportion with the margin of error
of 0.05, prefer a level of confidence of 95%, and has no estimate for the population proportion. (so we use
the probability is 0.50 or 50%) What is the required sample size?

- Determine the formula.

- Identify the value in each parameter.

- The sample size is

Answer 1

Answer: The student in the previous example also wants to estimate the proportion of cities that have private refuse collectors. The students wants to estimate the population proportion with the margin of error of 0.05, prefer a level of confidence of 95%, and has no estimate for the population proportion. (so we use the probability is 0.50 or 50%) What is the required sample size?

Solution:

we do not have estimate for the population proportion.

Let p = 0.50

1- p = 1 - 0.5 = 0.50

At 95% confidence level α =0.05.

Zα/2 = Z(0.025) = 1.96

The margin of error is E = 0.05

The formula for the sample size n:

n = (Zα/2 / E)2 * p(1-p)

n = (1.96/0.05)2 * 0.50 * 0.50

n = 384.16

∴ n = 385

Therefore, the required sample size is 385.